Tell AE that the footage is premultipled versus black (right click one the fototage to change its options). Oldest thing in 2d graphics, stuff you should know by the way, and yes its decribed in the manual. See threes 2 ways of storing alpha and the computer needs to know which brand the image uses.
One uses
upper layer color* upper layer alpha+ lower layer color *(1 - upper layer alpha)
thsi is called straight alpha whereas premultiplied (on black) alpha uses.
upper layer color+lower layer color *(1 - upper layer alpha)
The bonus withe the lower alternative is not the speed per see, not anymore. Rather, you can apprise alpha without actually inserting alpha and using background. Further sampling systems like 3d renders use normal signal functions that tend to produce this data so converting it to straight is a extra job pass. Making it easier to handle custom channels data. After all the 4 channels may not actually be RGBA but something totally independent (such as uv and the 2 bi normals wich don't intermix as signals) and you don't want to screw that up as a signal so your alpha is free to do other things.
On that note you can tell maya to do straight alpha but youll be wasting time doing that as a general rule. And offcourse you can screw things up equally wall with those custom channels.
So now you know
PS: yes i know people want sort of options that they dont have opttions to feel secure but all functionality or choice comes as price and ultimately the production might not want to take that confinement